This study aims to explore the bioconvective flow of a Casson–Williamson penta-hybrid nanofluid across an exponentially stretching permeable surface. The analysis accounts for the joint effects of a magnetic field, porous medium, thermal radiation, Brownian motion, thermophoresis, heat generation and chemical reaction on the transport behavior.
The physical problem is described through the governing partial differential equations for momentum, energy, concentration and the movement of motile microorganisms. Suitable similarity transformations reduce these dimensional equations into a coupled set of nonlinear ordinary differential equations, which are then solved numerically using the bvp4c technique in MATLAB. To complement the numerical work, an artificial neural network based on the Levenberg–Marquardt Algorithm (ANN-LMA) and a physics-informed NN (PINN) framework are constructed to predict the Nusselt number across mono-hybrid, tri-hybrid, tetra-hybrid and penta-hybrid nanoparticle systems.
The results reveal that increasing the magnetic field, porosity, Casson and Williamson parameters slows the fluid motion, while thermal radiation, Brownian motion, thermophoresis and heat generation raise the temperature within the boundary layer. The density of motile microorganisms falls as the Lewis and Peclet numbers grow. A comparative assessment shows that the penta-hybrid nanofluid outperforms the mono-hybrid, tri-hybrid and tetra-hybrid systems in heat transfer, mass transport and microorganism flux, a consequence of the stronger interaction among the dispersed nanoparticles.
Both the ANN-LMA and PINN models achieve very low mean squared error values and align closely with the numerical solutions, capturing the heat transfer response with notable precision. This work highlights the practical importance of penta-hybrid nanofluids and neural-network-based prediction tools for advanced thermal engineering and bioconvective transport applications. The ANN-LMA and PINN models achieved correlation coefficients close to unity (R1) and MSEs of the order of 10−10, confirming excellent predictive accuracy.
